As a method of extracting features to identify a person from a face image, there is a method in which an attention is directed to personal differences of shapes and arrangements of parts of a face, such as eyes, a nose, a mouth and the like, and features are extracted from them to be used in recognition. However, it is difficult to extract the parts of the face from the face image at a good precision. Even if the respective parts are successfully extracted, it is not easy to use the difference between the similar shapes in the recognition.
“Pattern recognition” written by Duda, Hart, and Stork (translation supervised by Onoe) discloses as a method extracting features to identify a person from a face image, a method using a principal component analysis and a method of using a discriminant analysis (refer to a non patent literature 1).
The principal component analysis is a typical multivariate analysis method that describes features of variances of a plurality of pieces of data by using the smallest possible number of indices (principal components) under the small loss of information. In the principal component analysis, information with regard to classes to which respective data belong is not used, and targets to be outputted are not determined in advance. For this reason, the principal component analysis is not always a preferred method as the method of extracting effective features to identify a person.
On the other hand, in the discriminant analysis, learning data are classified in advance, a distance of data between classes is determined based on information with regard to classes to which respective data belong. For example, learning is carried out such that a distance of data of the same class is reduced and a distance of data of different classes is extended. In the discriminant analysis, a normal distribution of input data is assumed. Thus, when input data have a distribution other than the normal distribution, a sufficient identification performance cannot be obtained.
In addition, personal authentication apparatus, in which an authentication error is reduced by the improvement of a precision in authenticating a person based on a face image, is described in Japanese Patent Publication (JP-P 2004-192250A) (refer to a patent literature 1), Japanese Patent Publication (JP-P 2007-128262A) (refer to a patent literature 2) and Japanese Patent Publication (JP-P 2007-156944A) (refer to a patent literature 3).
Japanese Patent Publication (JP-P 2001-184509A) proposes a pattern recognition method that handles an image itself as a pattern (refer to a patent literature 4). In the recognition of image data by using the pattern recognition method, without using knowledge peculiar to a face, the pattern recognition of the image data is carried out through learning similar to the discriminant analysis. However, when face image data is used, a distance suitable for identification is different from class to class. For this reason, when face image data of an unknown class is inputted, a high recognition precision cannot be obtained by this method.